Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · gr-qc/0506069

Rigorous steps towards holography in asymptotically flat spacetimes

C. Dappiaggi·V. Moretti·N. Pinamonti
View original source ↗Read source document ↗Export metadata ↓

Abstract

Scalar QFT on the boundary $\Im^+$ at null infinity of a general asymptotically flat 4D spacetime is constructed using the algebraic approach based on Weyl algebra associated to a BMS-invariant symplectic form. The constructed theory is invariant under a suitable unitary representation of the BMS group with manifest meaning when the fields are interpreted as suitable extensions to $\Im^+$ of massless minimally coupled fields propagating in the bulk. The analysis of the found unitary BMS representation proves that such a field on $\Im^+$ coincides with the natural wave function constructed out of the unitary BMS irreducible representation induced from the little group $Δ$, the semidirect product between SO(2) and the two dimensional translational group. The result proposes a natural criterion to solve the long standing problem of the topology of BMS group. Indeed the found natural correspondence of quantum field theories holds only if the BMS group is equipped with the nuclear topology rejecting instead the Hilbert one. Eventually some theorems towards a holographic description on $\Im^+$ of QFT in the bulk are established at level of $C^*$ algebras of fields for strongly asymptotically predictable spacetimes. It is proved that preservation of a certain symplectic form implies the existence of an injective $*$-homomorphism from the Weyl algebra of fields of the bulk into that associated with the boundary $\Im^+$. Those results are, in particular, applied to 4D Minkowski spacetime where a nice interplay between Poincaré invariance in the bulk and BMS invariance on the boundary at $\Im^+$ is established at level of QFT. It arises that the $*$-homomorphism admits unitary implementation and Minkowski vacuum is mapped into the BMS invariant vacuum on $\Im^+$.

Explore related subjects

gr-qchep-thmath-phmath.MP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

C. Dappiaggi, V. Moretti, N. Pinamonti. 2006-05-18. Rigorous steps towards holography in asymptotically flat spacetimes. https://doi.org/10.1142/s0129055x0600270x

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Photon propagation and black hole imaging in Kruglov nonlinear electrodynamics

Nonlinear electrodynamics (NLED) modifies photon propagation through an effective optical geometry, allowing optical phenomena to deviate from those predicted solely by the underlying spacetime metric. In this work, we revisit the Kruglov model, which generalizes Born--Infeld electrodynamics, and investigate the corresponding null geodesics in theeffective geometry through direct numerical integration, without relying on strong-field analytical approximations. We analyze the resulting photon spheres, gravitational lensing, black-hole shadows, and thin accretion-disk images, together with their dependence on the parameter $q$. For sufficiently small positive $q$, the effective angular metric develops a pole that generates stable photon orbits outside the event horizon and locally reverses the azimuthal evolution of photon trajectories, producing a distinctive bending pattern that resembles, although does not originate from, frame dragging. Conversely, negative $q$ introduces a zero of the effective correction factor, which acts as a turning point for photon trajectories and prevents them from entering the region where the background metric becomes complex. It produces measurable changes in light deflection, shadow radius, photon-ring morphology, and relativistic images. In particular, smaller positive values of $q$ produce thinner photon rings and enlarged shadow radii, whereas negative values generally lead to broader photon rings and smaller shadows. Comparison with the current Event Horizon Telescope constraints on Sgr~A* shows that a substantial region of the Kruglov parameter space remains compatible with present observations.

gr-qc↗
arXiv2026

Parity-dependent wave absorption and optical characteristics of a cored magnetic black hole

We study light propagation and coupled gravitational--electromagnetic waves around a black hole supported by a nonlinear magnetic field. The same field action fixes the geometry, the mass--charge relation, and the wave potentials. We calculate two critical impact parameters for light and solve the coupled scattering equations in both parity sectors. In eight solutions of one action, the two optical scales differ by $3.6$--$7.2\%$. The wave absorption also depends on parity. For $\ell=2$, the gap between the larger absorption eigenvalues reaches about $9.0$ percentage points. A wider frequency scan reveals a stronger effect in the second eigenchannel. The difference between the two absorption traces reaches $24.3$ percentage points. The trace equals twice the absorption of an equal incoherent mixture of incoming gravitational and electromagnetic fields. A controlled test of the wave operator shows that the nonlinear electromagnetic factor $κ$ plays an important role in the parity gap. We also examine four $\ell=3$ cases and use charge-matched Reissner--Nordström black holes as a separate control. The optical and wave calculations provide two complementary properties of the same magnetic source.

gr-qc↗
arXiv2026

Perturbative dynamics and relativistic effects of a dyonic Kalb-Ramond black hole

We investigate perturbative dynamics, tidal effects, and relativistic frequency shifts in a dyonic Kalb-Ramond black hole generated by a Lorentz-violating antisymmetric tensor background. The geometry is controlled by the mass $M$, the electric charge $Q$, the magnetic charge $p$, and the Lorentz-violating parameter $\ell$, with the dyonic sector entering through the effective combination $P_{\ell}^{2}=Q^{2}/(1-\ell)^{2}+p^{2}/(1-2\ell)$. First, we analyze the gravitational Doppler effect for radial signal exchange between freely falling and static observers, showing how the dyonic charges weaken the redshift by shifting the frequency ratio toward unity. We then compute the radial and angular tidal forces in a freely falling frame and determine the characteristic radii at which the usual stretching and compression patterns are reversed. The gravitational time delay is also evaluated for null trajectories, showing that the electric and magnetic sectors reduce the delay relative to the reference configuration. In the perturbative sector, we study massless scalar, vector, and spinor test fields together with an effective axial metric model, computing sixth-order WKB spectra and independently checking selected modes using the asymptotic iteration method. At fixed mass and charges, increasing the Lorentz-violating parameter raises the tabulated oscillation frequencies and damping rates in the original time coordinate; their interpretation accounts for time normalization and changes in effective parameters. The independent comparisons support the tested higher-multipole fundamental modes. Time-domain evolutions exhibit damped ringdown followed by power-law tails, whose exponents are estimated through fits incorporating finite time corrections and numerical sensitivity checks.

gr-qc↗